The two tranny codes 34 35 are due to the speed sensors not sensing the known values for any certain RPM. They know what the rpm in the front of the trans. through any certain gear (in this case 4 and 5) should be at the rear of the transmission. Seems likely that it's the speed sensors on the tranny or the ESM itself causing the issue. If not it would be mechanical and likely need a rebuild. It seems according to many sources and my mechanic friend that the sensors on this transmission are known to be a failure point and they are what gives the shifting module all it's information. You can see the sensors if you lay under the commander on the drivers side and look up at the transmission. They have two wires going into a round plastic connection into the transmission. Jeep has them for about 60ish.
Those are pretty much my same issues as well and I'm fairly sure it's either the sensors of slipping inside the tranny requiring a rebuild.